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# Communications in Number Theory and Physics

## Volume 9 (2015)

### Number 2

### Fourier coefficients of three-dimensional vector-valued modular forms

Pages: 387 – 411

DOI: http://dx.doi.org/10.4310/CNTP.2015.v9.n2.a5

#### Author

#### Abstract

We prove that only a finite number of three-dimensional, irreducible representations of the modular group admit vector-valued modular forms with bounded denominators. This provides a verification, in the three-dimensional setting, of a conjecture concerning the Fourier coefficients of noncongruence modular forms, and reinforces the understanding from mathematical physics that when such a representation arises in rational conformal field theory, its kernel should be a congruence subgroup of the modular group.

#### 2010 Mathematics Subject Classification

11F30, 11F99